Corrugated horn antennas were developed to provide circularly symmetrical patterns which are virtually free of primary sidelobes. These antennas have been quite successful but have been limited in bandwidth to approximately 2:1.
In the January 1973 edition of "Microwaves" and article appears on pages 44-49 entitled "Corrugations Lock Horns With Poor Beamshapes" in which it is taught that to design a corrugated horn the slot depth should be greater than a quarter of a wavelength at the low end of the frequency band and less than a half wavelength at the high end. This constraint common to all prior corrugated horn antennas limits the bandwidth thereof to less than 2:1.
The above referred to article also teaches that the slot width should be about a tenth of a wavelength at the low end of the frequency band and the spacing between the slots should be a quarter wavelength at the high end of the band. This will result in a corrugation pattern with the slots being less than a half of the available material.
Because of the above constraints, corrugated horn antennas have not been available to obtain a circularly symmetrical pattern where a constant beamwidth is required over a band width of greater than 2:1.